Atkin-Lehner |
3+ 5+ 7- 13+ 31- |
Signs for the Atkin-Lehner involutions |
Class |
42315a |
Isogeny class |
Conductor |
42315 |
Conductor |
∏ cp |
8 |
Product of Tamagawa factors cp |
deg |
12032 |
Modular degree for the optimal curve |
Δ |
8251425 = 32 · 52 · 7 · 132 · 31 |
Discriminant |
Eigenvalues |
-1 3+ 5+ 7- 2 13+ 6 -8 |
Hecke eigenvalues for primes up to 20 |
Equation |
[1,1,1,-126,474] |
[a1,a2,a3,a4,a6] |
Generators |
[-6:35:1] |
Generators of the group modulo torsion |
j |
221335335649/8251425 |
j-invariant |
L |
2.7802300149122 |
L(r)(E,1)/r! |
Ω |
2.3113553199897 |
Real period |
R |
0.60142851920615 |
Regulator |
r |
1 |
Rank of the group of rational points |
S |
0.99999999999673 |
(Analytic) order of Ш |
t |
2 |
Number of elements in the torsion subgroup |
Twists |
126945r1 |
Quadratic twists by: -3 |